On UNIX and Linux the superuser is called root. Root means getting root access so you can change anything in the system. Normally you run as a non root user so you avoid accidental deletion of system files. A root app like gingerbreak gives you root access, usually impossible by design of the manufacturer. Rooting lets you delete unwanted bloatware, install google market, etc.

With a Jailbroken iPhone the biggest advantage is installing 3rd party apps. With an Android device you can already install 3rd party apps. However, rooting gives you even more control to run more powerful apps and to even modify Android itself in a lot of neat ways.